Using small-angle X-ray scattering (SAXS), we have studied the initial stage (nucleation and oligomerization) of actin polymerization induced by raising temperature in a stepwise manner from 1&deg;C to 30&deg;C at low ionic strength (4.0 mg ml&minus;1 actin in G-buffer). The SAXS experiments were started from the mono-disperse G-actin state, which was confirmed by comparing the scattering pattern in q- and real space with X-ray crystallographic data. We observed that the forward scattering intensity I(q &rarr; 0), used as an indicator for the extent of poly-merization, began to increase at &sim;14&deg;C for Mg-actin and &sim;20&deg;C for Ca-actin, and this critical temperature did not depend on the nucleotide species, i.e., ATP or ADP. At the temperatures higher than &sim;20&deg;C for Mg-actin and &sim;25&deg;C for Ca-actin, the coherent reflection peak, which is attributed to the helical structure of F-actin, appeared. The pair-distance distribution functions, p(r), corresponding to the frequency of vector lengths (r) within the molecule, were obtained by the indirect Fourier transformation (IFT) of the scattering curves, I(q). Next, the size distributions of oligomers at each temperature were analyzed by fitting the experimentally obtained p(r) with the theoretical p(r) for the helical and linear oligomers (2&ndash;13mers) calculated based on the X-ray crystallographic data. We found that p(r) at the initial stage of polymerization was well accounted for by the superposition of monomer, linear/helical dimers, and helical trimer, being independent of the type of divalent cations and nucleotides. These results suggest that the polymerization of actin in G-buffer induced by an increase in temperature proceeds via the elongation of the helical trimer, which supports, in a structurally resolved manner, a widely believed hypothesis that the polymerization nucleus is a helical trimer.

f5-6_1: Structural characterization of actin aggregates at the initial stage of polymerization.Analysis of the experimental p(r) at T∼T* assuming the mixture model of a monomer (M), a linear dimer (L2), a helical dimer (H2), and a helical trimer (H3): (a), Ca-ATP at 20°C, and (b), Mg-ATP at 13°C. (b) and (d), The examined 100 parameter sets for different weight fractions of H2, L2, and H3 (WH2, WL2 and WH3) and their R2 values obtained as a function of the monomer weight fraction (WM). (a) and (c), The experimental p(r) (open black circles) and the fitting curve (pink solid line) based on the superposition of the simulated p(r) functions of M, L2, and H3 (sequential solid lines, orange, blue and red, respectively). In the insets of the panels (a) and (c), the experimental scattering intensity I(q) and the fitting curve using I(q) simulated from the crystal data are shown. This confirms simultaneous successful description of the scattering data in both q-space and a real space. Solid arrows indicate the minimal values of R2. Dashed arrows indicate R2 for the parameter sets that correspond to the panels (a) and (c).

Mentions:
As shown in Figure 5, we found that p(r) of the initial stage of polymerization (T∼T*) was well accounted for by the superposition of either M, L2, H2, and H3, or M, L2, and H3 with a smaller number of the adjustable parameters. A pathway of the helical trimer (H3) formation, namely, whether it is M→L2/H2→H3 or M→L2→H3, cannot be decisively established from the present analysis. Nevertheless, we infer that M→L2→H3 may be a more plausible nucleation pathway, because the weight fraction of L2 is always greater than that of H2, and, as highlighted by solid arrows in Fig. 5, the minimum of R2 was attained at the distribution that was very close to M+L2+H3 for both Ca-ATP and Mg-ATP. We note that these data do not exclude the possibility of the co-existing M→H2→H3. As described in the following section, at the next temperature step, where the temperature is increased by 1°C, the features of the experimental p(r) were mostly governed by the presence of long polymers. The fact implies that the elongation into long helical oligomers is triggered by the formation of a helical trimer (H3). The experimental scattering intensity I(q) and the fitting curve using the simulated I(q) from the crystallographic data were also very similar (see insets in Fig. 5a and c). This confirms that the scattering data are successfully described both in q- and real space.

f5-6_1: Structural characterization of actin aggregates at the initial stage of polymerization.Analysis of the experimental p(r) at T∼T* assuming the mixture model of a monomer (M), a linear dimer (L2), a helical dimer (H2), and a helical trimer (H3): (a), Ca-ATP at 20°C, and (b), Mg-ATP at 13°C. (b) and (d), The examined 100 parameter sets for different weight fractions of H2, L2, and H3 (WH2, WL2 and WH3) and their R2 values obtained as a function of the monomer weight fraction (WM). (a) and (c), The experimental p(r) (open black circles) and the fitting curve (pink solid line) based on the superposition of the simulated p(r) functions of M, L2, and H3 (sequential solid lines, orange, blue and red, respectively). In the insets of the panels (a) and (c), the experimental scattering intensity I(q) and the fitting curve using I(q) simulated from the crystal data are shown. This confirms simultaneous successful description of the scattering data in both q-space and a real space. Solid arrows indicate the minimal values of R2. Dashed arrows indicate R2 for the parameter sets that correspond to the panels (a) and (c).

Mentions:
As shown in Figure 5, we found that p(r) of the initial stage of polymerization (T∼T*) was well accounted for by the superposition of either M, L2, H2, and H3, or M, L2, and H3 with a smaller number of the adjustable parameters. A pathway of the helical trimer (H3) formation, namely, whether it is M→L2/H2→H3 or M→L2→H3, cannot be decisively established from the present analysis. Nevertheless, we infer that M→L2→H3 may be a more plausible nucleation pathway, because the weight fraction of L2 is always greater than that of H2, and, as highlighted by solid arrows in Fig. 5, the minimum of R2 was attained at the distribution that was very close to M+L2+H3 for both Ca-ATP and Mg-ATP. We note that these data do not exclude the possibility of the co-existing M→H2→H3. As described in the following section, at the next temperature step, where the temperature is increased by 1°C, the features of the experimental p(r) were mostly governed by the presence of long polymers. The fact implies that the elongation into long helical oligomers is triggered by the formation of a helical trimer (H3). The experimental scattering intensity I(q) and the fitting curve using the simulated I(q) from the crystallographic data were also very similar (see insets in Fig. 5a and c). This confirms that the scattering data are successfully described both in q- and real space.

Using small-angle X-ray scattering (SAXS), we have studied the initial stage (nucleation and oligomerization) of actin polymerization induced by raising temperature in a stepwise manner from 1&deg;C to 30&deg;C at low ionic strength (4.0 mg ml&minus;1 actin in G-buffer). The SAXS experiments were started from the mono-disperse G-actin state, which was confirmed by comparing the scattering pattern in q- and real space with X-ray crystallographic data. We observed that the forward scattering intensity I(q &rarr; 0), used as an indicator for the extent of poly-merization, began to increase at &sim;14&deg;C for Mg-actin and &sim;20&deg;C for Ca-actin, and this critical temperature did not depend on the nucleotide species, i.e., ATP or ADP. At the temperatures higher than &sim;20&deg;C for Mg-actin and &sim;25&deg;C for Ca-actin, the coherent reflection peak, which is attributed to the helical structure of F-actin, appeared. The pair-distance distribution functions, p(r), corresponding to the frequency of vector lengths (r) within the molecule, were obtained by the indirect Fourier transformation (IFT) of the scattering curves, I(q). Next, the size distributions of oligomers at each temperature were analyzed by fitting the experimentally obtained p(r) with the theoretical p(r) for the helical and linear oligomers (2&ndash;13mers) calculated based on the X-ray crystallographic data. We found that p(r) at the initial stage of polymerization was well accounted for by the superposition of monomer, linear/helical dimers, and helical trimer, being independent of the type of divalent cations and nucleotides. These results suggest that the polymerization of actin in G-buffer induced by an increase in temperature proceeds via the elongation of the helical trimer, which supports, in a structurally resolved manner, a widely believed hypothesis that the polymerization nucleus is a helical trimer.